w(w+10)50=180

Solution for w(w+10)50=180 equation:

Simplifying
w(w + 10) * 50 = 180

Reorder the terms:
w(10 + w) * 50 = 180

Reorder the terms for easier multiplication:
50w(10 + w) = 180
(10 * 50w + w * 50w) = 180
(500w + 50w2) = 180

Solving
500w + 50w2 = 180

Solving for variable 'w'.

Reorder the terms:
-180 + 500w + 50w2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 500w + 50w2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-18 + 50w + 5w2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-18 + 50w + 5w2)' equal to zero and attempt to solve:

Simplifying
-18 + 50w + 5w2 = 0

Solving
-18 + 50w + 5w2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-3.6 + 10w + w2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + 10w + 3.6 + w2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + 10w + w2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + 10w + w2 = 0 + 3.6
10w + w2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
10w + w2 = 3.6

The w term is 10w.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10w + 25 + w2 = 3.6 + 25

Reorder the terms:
25 + 10w + w2 = 3.6 + 25

Combine like terms: 3.6 + 25 = 28.6
25 + 10w + w2 = 28.6

Factor a perfect square on the left side:
(w + 5)(w + 5) = 28.6

Calculate the square root of the right side: 5.347896783

Break this problem into two subproblems by setting 
(w + 5) equal to 5.347896783 and -5.347896783.

Subproblem 1
w + 5 = 5.347896783

Simplifying
w + 5 = 5.347896783

Reorder the terms:
5 + w = 5.347896783

Solving
5 + w = 5.347896783

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + w = 5.347896783 + -5

Combine like terms: 5 + -5 = 0
0 + w = 5.347896783 + -5
w = 5.347896783 + -5

Combine like terms: 5.347896783 + -5 = 0.347896783
w = 0.347896783

Simplifying
w = 0.347896783

Subproblem 2
w + 5 = -5.347896783

Simplifying
w + 5 = -5.347896783

Reorder the terms:
5 + w = -5.347896783

Solving
5 + w = -5.347896783

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + w = -5.347896783 + -5

Combine like terms: 5 + -5 = 0
0 + w = -5.347896783 + -5
w = -5.347896783 + -5

Combine like terms: -5.347896783 + -5 = -10.347896783
w = -10.347896783

Simplifying
w = -10.347896783

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.347896783, -10.347896783}
Solution
w = {0.347896783, -10.347896783}